The fourth-seeded Osaka never faced a break point and beat the 14th-seeded Kontaveit 6-3, 6-4 in Arthur Ashe Stadium on Sunday.
Osaka owns two Grand Slam titles, including Flushing Meadows in 2018. She lost in the fourth round a year ago.
Kontaveit won the match's first point but followed that with a pair of double-faults and then a pair of backhand errors to get broken.
And Osaka was on her way, winning 35 of 45 service points.
The 22-year-old from Japan improved to 5-0 head to head against Kontaveit and now faces unseeded Shelby Rogers of the United States in the quarterfinals.
Rogers has won all three matches she has played against Osaka.
Also on Sunday, Jennifer Brady extended her dominant showing at the US Open and reached the quarterfinals for the first time.
The hard-hitting 25-year-old knocked off Angelique Kerber 6-1, 6-4. The 41st-ranked Brady used her dominant forehand to take control in a 22-minute first set.
"Wow,'' she said, describing the moment. "Just wow.''
Brady has yet to drop a set and has lost only 19 games in her four matches.
For Kerber, it was an abrupt end to a resurgent week. The 2016 US Open champion couldn't make headway against Brady's consistently solid serve and groundstrokes.
The 93rd-ranked Rogers upset sixth-seeded Petra Kvitova 7-6 (5), 3-6, 7-6 (6) for her second berth in a Grand Slam quarterfinal and her first at Flushing Meadows.
"It's so special,'' Rogers said.
Brady took a medical timeout while leading 3-2 in the second set to get her left leg treated. She returned to the court with her upper leg wrapped and finished the match in 1 hour, 28 minutes -- her longest of the tournament.
"My leg was bothering me, and I wasn't serving well,'' said Brady, who is based in Florida. "I was glad to close it out.''
A former UCLA standout, Brady becomes the first women's college player to reach the quarterfinals at the US Open since Gigi Fernandez in 1994. Brady also won her first WTA title last month at the Top Seed Open, which was the first professional tennis event in the United States since the start of the coronavirus pandemic.
"She's hitting the ball really fast,'' Kerber said. "She's playing well. She has confidence. Let's see how far she can get here, but for sure she can get far.''
Putintseva is in her third Grand Slam quarterfinal (2016, '18 French Open) after her win over Martic.
She threw her racket to the ground after dropping the second set, a moment of frustration that became her turning point. The 35th-ranked player recovered to beat Martic and earn her first berth in a US Open quarterfinal.
"Before the third set I said to myself, 'Whatever happens, you just make it difficult for her, you're not going to make any mistakes, you're going to move her around the court as much as possible,''' Putintseva said.
Putintseva has been the best in the women's bracket at breaking serve, and she converted 4 of 9 chances.
Martic took a medical timeout to get her left foot treated and wrapped before the final game of the match. She finished with 39 unforced -- 14 more than Putintseva.
The Associated Press contributed to this report.